Find the domain and the range of the function `y=f(x)`, where `f(x)` is given by
`log_(10)(x)`.

Answer

To find the domain and range of the function \( y = f(x) \), where \( f(x) = \log_{10}(x) \), we can follow these steps:

### Step 1: Identify the Domain
The logarithmic function \( \log_{10}(x) \) is defined only for positive values of \( x \). This means that \( x \) must be greater than 0.

**Domain**:
\[ x > 0 \quad \text{or in interval notation, } (0, \infty) \]

### Step 2: Identify the Range
The output of the logarithmic function can take any real number value. As \( x \) approaches 0 from the right, \( \log_{10}(x) \) approaches negative infinity. As \( x \) increases, \( \log_{10}(x) \) increases without bound, approaching positive infinity.

**Range**:
\[ y \in (-\infty, \infty) \]

### Final Answer
- **Domain**: \( (0, \infty) \)
- **Range**: \( (-\infty, \infty) \)

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